Massachusetts US Senator Elizabeth Warren would bloody more than just former Red Sox great Curt Schilling’s sock — politically — if the Democrat and Republican both run in 2018.

That’s according to a new Suffolk University/Boston Globe poll that found Warren leading Schilling 58 percent to 24 percent among 500 likely voters.

In the survey, which was conducted Monday through Wednesday, 16 percent were undecided about the hypothetical matchup in two years.

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Warren, the liberal superstar, hasn’t said if she’s running for a second term. Schilling, an outspoken conservative, has said he is going to run for the seat, presuming his wife, Shonda, gives him the green light.

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Of course, two years is an eon in politics. And it’s not unusual for challengers to be trailing this far out from Election Day. But Schilling is well-known for a might-be GOP statewide candidate. He was a key pitcher in the Boston Red Sox’s curse-reversing 2004 World Series victory.

(John W. Henry was then, and is now, the principal owner of the baseball team. He currently also owns The Boston Globe.)

Despite his place in Sox lore, Schilling is not seen warmly by Massachusetts likely voters. Forty-one percent of likely voters have an unfavorable opinion of him, while only 18 percent have a favorable view of him. Twenty-eight percent are undecided and 14 percent have never heard of him.

Warren, on the other hand, is seen favorably by 56 percent of likely voters and unfavorably by 31 percent.

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An even more popular figure in blue Massachusetts? Republican Governor Charlie Baker. He’s seen favorably by 64 percent of likely voters and unfavorably by only 12 percent, solid numbers for a pol who has been in office since January 2015.

On a different, but related measure, Baker also excels. Sixty-nine percent of those polled approve of the job he is doing as governor, while 10 percent disapprove and 19 percent are undecided.

President Obama doesn’t score quite as well with the voters of the Commonwealth: 63 percent approve of the way the president is handling his job, while 29 percent disapprove.

But he is seen warmly by voters here: 67 percent have a favorable view of him, while 27 percent have an unfavorable view.

Also in the new poll — which carries a margin of error of plus-or-minus 4.4 percentage points — news that probably won’t surprise you: Democrat Hillary Clinton is poised to win Massachusetts’ 11 electoral votes.